Application of electrical energy in modern times often involves rechargeable batteries. Every household or place of business typically has several devices that operate from rechargeable batteries.
A promising technology for rechargeable batteries that has been employed in numerous applications is based on electro-chemical reactions involving Lithium. The so-called Lithium-Ion (Li-Ion) batteries of many different arrangements and material composition have been designed and used worldwide.
These batteries are typically lighter and store more energy in a given volume than the batteries based on the previous technologies, such as Lead-Acid, Nickel-Cadmium, etc.
The Lithium-chemistry batteries are, however, sensitive to over-charging that may lead to spontaneous and irreversible overheating and even fire/explosion.
At the same time, the Li-Ion cells are sensitive to over-discharge, as irreversible electro-chemical reactions take place and the cells quickly lose their ability to store charge (e.g. the capacity of the cells gets quickly reduced).
In order to store significant amounts of electrical energy, the individual Li-Ion cell are typically organized into batteries that contain series-connected cell. Since all the cells receive the same charging current, if a single cell reaches its maximum charge, the charging current must be stopped in order to prevent overcharging of that single cell. However, the rest of the cells will at that point not yet have received the full charge. After several charge/discharge cycles, it may well be that the whole battery becomes totally unusable, as some cells are totally discharged.
That is why it is typical that the Li-Ion battery includes some kind of equalization circuit that tries to “balance” the whole battery, allowing it to have useful life that is much longer that just several charge/discharge cycles, typically allowing hundreds or even thousands of cycles.
Thus the balancing circuit is an important building block for utilization of the Li-Ion batteries.
There are two types of balancing circuits, referring to the ability of the circuit to remove energy from one cell and deposit the energy in another cell (a so-called active balancing), and operations where the energy is simply dissipated as heat if a cell is close to overcharging (called passive or dissipative balancing).
An active balancing scheme is preferable not only due to the energy savings reasons (so as to reduce the energy costs), but also for the reduction of the heat generated in the battery; the heat having a detrimental effect on the useful life of the battery.
An example of passive balancing is shown in FIG. 1a. 
Dissipative Balancing. A number of cells 1, each cell having corresponding Resistor 2 and Switch 3 (that is typically a semiconductor device controlled by the monitoring circuitry), are connected in series. While charging, if a cell's potential gets close to the voltage that indicates full charge, at a time when the rest of the cells are not fully charged, a Switch 3 for that cell is activated (closed), and the current flowing via Resistor 2 discharges the cell. Depending on the magnitude of the discharge current flowing via Resistor 2, it may or may not be necessary to interrupt the “main” charging current through the whole battery.
Obviously, this method results in high heat losses. This method can produce a balanced state of the battery only while the battery is charging, and typically only for a condition of full charge. When the battery is discharged, as soon as one cell reaches the minimum allowed voltage potential, the whole battery is considered discharged and not able to provide any more energy. At the same time, other cells in the battery may well have significant amounts of energy left; however the Dissipative Balancing scheme does not allow recovery of this energy.
Another method is shown in FIG. 1b. 
Chain Balancing. The two-cell balancing circuit 4 is able to transfer charge from one cell to the next cell in the series-connected stack of cells. While the method can formally be called “active balancing” due to energy transfer from one cell to the next (rather than dissipating the excess energy as heat), in reality the resulting heat losses during operations of the circuits of this type are high. It will be readily recognized that the energy transfer by this “chain” method is only efficient if the cells that need to be balanced are located close to each other in the series-connected string. On the other hand, if a cell with higher voltage is located relatively far from the cell that is having a lower voltage (e.g. having several cells in the chain between them), then the total efficiency for the power transfer will be the product of efficiency for all the transfers that are needed to move the energy from higher-charged cell to the lower-charged cell. For example, if the two-cell balancing circuit has 80% efficiency, and there are five cells between the cells that need to exchange the energy, then the resulting efficiency will only be about 26% (0.8*0.8*0.8*0.8*0.8*0.8=0.262).
In practical terms, there will be very little benefit in energy savings as compared with purely passive/dissipative balancing method, with significantly higher costs due to complexity of the two-cell balancing circuits.
Yet another active balancing scheme is depicted in FIG. 1c. 
Charge-only Balancing. A transformer having multiple windings over Core 6 is utilized to charge all the cells at the same time, with a natural result that the voltage of all the cells is the same. This “simultaneous” charging can occur in addition to a larger charging current that is flowing through the series-connected cells in the battery. It will be recognized that the diodes 5 that are needed in this circuit will prevent operations with high efficiency due to non-zero forward voltage drop in the semiconductor diode; in addition, this type of circuits only permits the addition of energy to cells, and can only be deployed if the whole battery is somewhat discharged; it is unsuitable if one of the cells has to be discharged rather than charged.
Many active balancing approaches require measurement of the state of charge of each cell, and control or manipulation of the balancing system to bring about balancing. It would be helpful if an approach could be found that was self-adjusting and self-correcting and did not rely upon measurement of the state of charge of each cell.
It would be helpful if a way could be found to provide balancing between cells that is more efficient than prior-art approaches, and that can offer its benefits during charging times, discharging times, and idle times.